Assuming the bond speculator wants to hedge her net bond position, what is the optimal number of...

A bond speculator currently has positions in two separate corporate bond portfolios: a long holding in Portfolio 1 and a short holding in Portfolio 2. All the bonds have the same credit quality. Other relevant information on these positions includes:

Portfolio

Bond

Market Value (Mil.)

Coupon Rate

Compounding Frequency

Maturity

Yield to Maturity

1

A

$6.00

0%

Annual

3 yrs

7.31%

B

4

0

Annual

14 yrs

7.31

2

C

11.5

4.6

Annual

9 yrs

7.31

Treasury bond futures (based on $100,000 face value of 20-year T-bonds having an 8 percent semiannual coupon) with a maturity exactly six months from now are currently priced at 109–24 with a corresponding yield to maturity of 7.081 percent. The “yield betas” between the futures contract and Bonds A, B, and C are 1.13, 1.03, and 1.01, respectively. Finally, the modified duration for the

T-bond underlying the futures contract is 10.355 years.

a. Calculate the modified duration (expressed in years) for each of the two bond portfolios. What will be the approximate percentage change in the value of each if all yields increase by 60 basis points on an annual basis?

b. Without performing the calculations, explain which of the portfolios will actually have its value impacted to the greatest extent (in absolute terms) by the shift yields. (Hint: This explanation requires knowledge of the concept of bond convexity.)

c. Assuming the bond speculator wants to hedge her net bond position, what is the optimal number of futures contracts that must be bought or sold? Start by calculating the optimal hedge ratio between the futures contract and the two bond portfolios separately and then combine them.